I have done some projects similar to this with a stick welder. After a couple of joints, you get a feel for just how to do it. Most of the joints turn out well. Those that do not can either be done again or ground to look better. I have also brazed some wire baskets used to suport tomato plants when the welds broke. Results were a little inconsistent and messy. I have not learned TIG, but would recommend it over brazing. I suspect the original bottle cages may have been spot welded.